since \(\beta _{k}^{\rm {}}s_k = A\mathbf {e}_k\)  for all \(k\) . This expression extends [1]}. To prove the convergence of the gradient method for strictly convex quadratic functions, it is sufficient to show that \(\Vert \mathbf {g}_k\Vert  \rightarrow 0\) . Since we chose an orthonormal basis, \(\Vert g_k\Vert ^2 = \sum _i (\gamma _{i}^{k})^2\)  and thus we aim to show \(\gamma _{i}^{k}\rightarrow 0\)  for \(i=1,\dots ,n\) . We remark that working with the \(\gamma _{i}^{k}\)  is equivalent to assume that our Hessian matrix \(A\)  is diagonal.
